Artistic genes course through Isca Greenfield-Sanders's slender form—her father, for one, is the celebrated portrait photographer Timothy Greenfield-Sanders. "I am the granddaughter of an Abstract Expressionist painter, the niece of a sculptor, the sister of a filmmaker, and the wife of a painter," says the New York artist. Yet numbers, of all things, have had just as powerful an influence—how many college grads do you know with a double major in mathematics and painting? "Math," the Brown alumna adds, "was my rebellion."

It's also the underpinning of Greenfield-Sanders's luminous large-scale paintings of outdoor family rituals that have taken the art world by storm. Each of her works is underlaid with a subtle grid of 7-inch squares, a precise and logical system to help counter what she calls art's "freeing and terrifying" lack of rules. Her process is as regimented as any equation. First, she scours eBay and upstate New York tag sales for slides of anonymous family scenes, such as birthday parties and vacations, from the 1950s and '60s. Anything more recent has "too much visual garbage," she explains, "like logos on T-shirts." The artist then scans and edits them, often deleting people until she is left with a solitary figure for a more formal, isolated effect. She reworks the resulting image with pencils and watercolors to create a small study that she enlarges and reprints in parts on rice paper. Each piece is then affixed like a tile to the canvas, forming a grid. Out come the oil paints, which she applies over the image, and what was generic and vaguely nostalgic becomes something utterly new—and a far cry from the original happy scene. Darkness lurks in the shadows (poolside hedges, for example, are often pitch-black), as if the upheavals of the coming decades are just across the fence.

The palette is luscious, inventive, and often abstract: bubble-gum-pink, for instance, for the ocean in her 2007 painting Red Boat Beach, 4 Kids. For Greenfield-Sanders, hues drastically affect the feeling of the painting. "The pink landscapes are otherworldly and hot—the temperature changes and so does the sense of alienation," she says. Often the paint is transparent, all the better to illuminate the original study underneath and retain the grid's mesmerizing geometry.

That layered complexity has attracted a strong following. San Francisco dealer John Berggruen was an early champion: After seeing her work in Aspen in 2002, he arranged for two solo shows at his eponymous gallery; later came dozens more throughout Europe and at the New York gallery Goff + Rosenthal. Avid collectors such as Ronald S. Lauder own her paintings, and she is represented in the collections of Houston's Museum of Fine Arts and the Guggenheim in New York. "Her work feels autobiographical on one level, yet there's also ambiguity and mystery," says Lisa Dennison, the Guggenheim's former director. "She's absorbed her father's lessons but has created something very new. Photography is her starting point, whereas for her father it's the end result. And they're just beautifully painted."

For a forthcoming show at Goff + Rosenthal in September, Greenfield-Sanders is working on a new series, of Korean and Second World War parachute jumpers. "Instead of water there's open sky," she explains, "so the treatment is similar to my beach paintings." She started out making them in blue and pink and more recently has turned to black for the background color. "It's dark," acknowledges the artist, who calls them her most political statement to date. "It's no coincidence that I'm painting these while we're at war." But, she adds, they also hold a wonderfully liberating promise: "You're in your parachute—and you're making your escape."